Solve 65m^7n^5/50m^4n^12

$$\frac { 65 m ^ { 7 } n ^ { 5 } } { 50 m ^ { 4 } n ^ { 12 } }$$

Evaluate

$$\frac{13m^{3}}{10n^{7}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{65^{1}m^{7}n^{5}}{50^{1}m^{4}n^{12}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{65^{1}}{50^{1}}m^{7-4}n^{5-12}$$

Subtract 4 from 7.

$$\frac{65^{1}}{50^{1}}m^{3}n^{5-12}$$

Subtract 12 from 5.

$$\frac{65^{1}}{50^{1}}m^{3}n^{-7}$$

Reduce the fraction \frac{65}{50} to lowest terms by extracting and canceling out 5.

$$\frac{13}{10}m^{3}\times \frac{1}{n^{7}}$$

Differentiate w.r.t. n

$$-\frac{91m^{3}}{10n^{8}}$$